Senator Ted Cruz has a message for fellow Republicans: It’s time to go to the mat to stop Obamacare, even if that means shuttering the government.

The Texan’s strategy is simple enough. Congress needs to pass a so-called continuing resolution to keep the government running by Sept. 30. Republicans, Cruz argues, should refuse to vote for the measure unless it prohibits spending any federal money on the President’s signature legislative accomplishment. If the stance sparks a shutdown, so be it.

“If we can actually get Republicans to stand up and fight,” Cruz told reporters over Chick-Fil-A sandwiches at a briefing sponsored by the conservative Heritage Foundation, “I believe we can win this fight.”

Note the target of the challenge. In the six months since swaggering into the Senate, the Tea Party firebrand has caused even more heartburn for his own side than he has for Democrats. Cruz was a leading voice in the legislative fight against comprehensive immigration reform, which many Republicans consider essential to the party’s ability to compete in presidential elections. His rough questioning during Chuck Hagel’s confirmation hearings drew rebukes from peers, which he later repaid by dubbing Republicans “squishes” and “scared.” To the conservative grassroots, Cruz is a budding hero; to some of his colleagues, he’s a showboat bent on using the Senate as a publicity platform rather than a lawmaking body.

Now, at a juncture when Republican leaders are leery of another round of budget brinkmanship, Cruz is inviting a showdown that could result in the party shouldering the blame for a shutdown. “It’s not going to be an easy fight,” he admitted. “But the question I would encourage you to ask of anyone doubting this strategy is: What is your alternative? … Should we just surrender?”

Cruz knows Democrats will pound the GOP for taking a position that threatens to shut down the government. But he argues a bruising confrontation is worth preventing crucial elements of health care reform, including insurance exchanges, from taking effect on Jan. 1. “No major entitlement, once it has been implemented, has ever been unwound,” he told reporters. “If we don’t do it now, in all likelihood we never will.”

Of course, Republicans have been vying to throttle the President’s signature legislative accomplishment since Congress passed it into law in March 2010. The House has voted more than three dozen times to roll back all or part of the law. In a swipe at fellow Republicans, Cruz admitted most of those efforts were little more than political theater. “Those votes were, by and large, empty, symbolic votes that had zero chance of passing,” Cruz said Tuesday.

Some Republican colleagues say the same of his own plan, which is also being spearheaded by conservative senators Marco Rubio of Florida and Mike Lee of Utah. “It requires 60 votes in the United States Senate [to achieve repeal, and] 67 votes to override a presidential veto,” says Senator John McCain, who recently dubbed Cruz a “wacko bird.” When informed of Cruz’s remarks, McCain—who was imprisoned and tortured during the Vietnam War—pretended to yank a white flag from the breast pocket of his suit. “Yeah, I’m scared,” he cracked, a tight smile frozen on his face. “I surrender.”

“They’re nervous about being blamed for a government shutdown,” Cruz said of skeptical colleagues. “To win this fight,” he added, “we have to make it riskier to do the wrong thing than it is to do the right thing.” That means applying grassroots pressure on fellow conservatives by generating hundreds of thousands of phone calls. The initiative could put powerful colleagues in a bind.

Take Republican Senate Leader Mitch McConnell. The Kentuckian is facing a primary challenge in his re-election bid next year, and could be vulnerable on the right if he doesn’t sign onto the push to defund the totemic law. On the other hand, McConnell is one of the leaders of the Republican Party, whose consultant class has widely concluded a shutdown would hurt the party, as it did in the mid-1990s. (McConnell sidestepped a reporter’s question Tuesday about the supported the effort, allowing only that “discussions continue.”)

Revisionist history, Cruz argues. “The cocktail chatter wisdom in Washington that the shutdown was a disaster for Republicans is not borne out by the data,” he said, noting Republicans dropped only a handful of House seats in 1996 and gained two in the Senate, even as Bill Clinton romped to re-election. Nor was the actual shutdown “as calamitous as many paint it,” according to Cruz. “The world didn’t end. Planes didn’t fall out of the sky. Social Security checks didn’t stop. We didn’t default on our national debt,” he said. “What happened was nonessential government services were temporarily suspended. That happens every single week. On the weekend.”

Cruz says the country is with him. But at least some poll numbers suggest otherwise. The American public remain bitterly split over the merits of the health-care law, with 40% of respondents in an April Kaiser Health Tracking poll saying they regard the law unfavorably and 35% supporting it. But by a 58% to 31% margin, respondents say they oppose stopping the health reform law by cutting off its funding. In addition, a new report from the nonpartisan Congressional Research Service indicates that “substantial” portions of the law would still be implemented in the event of a shutdown.

For now, most Republicans are parrying questions about a push that threatens to split the party over the next two months. “All Republicans would love to see Obamacare defunded,” says Republican John Thune of South Dakota, a member of the party’s Senate leadership team. “It just comes down to a difference in tactics.” The tactics they choose could have sweeping consequences for the GOP’s fortunes—and that of the country.